# Ch-6 : Microwave Travelling Wave Tubes O Type¶

## Page Number: 330 Example 6.1¶

In [16]:
from __future__ import division
from math import sqrt, pi
#Given

#Given
I0=30e-3  #A
V0=3e3  #V
Z0=10  #ohm
l=0.1624  #m
f=10e9  #Hz

#(i) Gain parameter
C=((I0*Z0)/(4*V0))**(1/3)
print 'Gain parameter: %0.3f'%C

N=(l*f)/(0.593e6*sqrt(V0))

#(ii) Power Gain
Ap=-9.54+(47.3*C*N)
print 'Power gain: %0.3f'%Ap,'dB'

ve=0.593e6*sqrt(V0)
be=(2*pi*f)/ve

#Four propogation constants
gam1=((-sqrt(3)*be*C)/2)+(1J*be*(2+C))/2
gam2=((sqrt(3)*be*C)/2)+(1J*be*(2+C))/2
gam3=1J*be*(1-C)
gam4=-1J*be*(1-((C*C*C)/4))

print 'Four propogation constants:\n {:.3f}\n{:.3f}\n{:.3f}\n{:.3f}\n'.format(gam1,gam2,gam3,gam4)

#Calculations for propogation constants are wrong in book for gam 3 and 4, hence answers dont match

Gain parameter: 0.029
Power gain: 59.613 dB
Four propogation constants:
-48.986+1962.764j
48.986+1962.764j
0.000+1877.917j
0.000-1934.469j



## Page Number: 332 Example 6.2¶

In [17]:

#Given
I0=20e-3  #A
V0=4e3  #V
Z0=100  #ohm
N=30

C=((I0*Z0)/(4*V0))**(1/3)
#Gain
Ap=-9.54+(47.3*C*N)
print 'Gain:' ,Ap,'dB'

Gain: 61.41 dB


## Page Number: 332 Example 6.3¶

In [19]:

#Given
c=3e8  #m/s
d=2e-3  #m
p=50e2  #turns per m
e=1.6e-19  #J
m=9.1e-31

# Axial phase velocity
vp=c/(pi*p*d)
print 'Axial phase velocity: %0.3f'%vp,'m/s'

#Anode voltage
V0=(m*vp*vp)/(2*e)
print 'Anode voltage: %0.3f'%V0, 'V'

Axial phase velocity: 9549296.586 m/s
Anode voltage: 259.319 V


## Page Number: 332 Example 6.4¶

In [20]:
from math import sin
#Given
c=3e8 #m/s
f=8e9  #Hz
al=2  #Np/m

#Phase velocity
vp=c*sin(a)

#Propogation constant
be=(2*pi*f)/vp

gam=al+(1J*be)
print 'Propogation constant: {:.3f}'.format(gam)

Propogation constant: 2.000+2183.964j


## Page Number: 333 Example 6.5¶

In [22]:

#Given
Vc=11e3  #V
Ir=0.85  #A
V0=31e3  #V
Pout=50e3  #W
I=7  #A

#Electronic efficiency
ne=Pout/(V0*I)
print 'Electronic efficiency: %0.3f'%(ne*100), '%'

#Overall efficiency
no=Pout/(Vc*(I-Ir))
print 'Overall efficiency: %0.3f'%(no*100), '%'

#Answer for elecytronic efficiency should be 23.04% but it is given as 36.4 in book

Electronic efficiency: 23.041 %
Overall efficiency: 73.910 %


## Page Number: 333 Example 6.6¶

In [23]:

#Given
I0=0.95  #A
V0=7e3  #V
Z0=20  #ohm
N=20

C=((I0*Z0)/(4*V0))**(1/3)
#Gain
Ap=-9.54+(47.3*C*N)
print 'Gain: %0.3f'%Ap,'dB'

Gain: 73.590 dB


## Page Number: 334 Example 6.7¶

In [24]:

#Given
Vc=12e3  #V
V0=30e3  #V
Pout=60e3  #W
I=7.5  #A

#Electronic efficiency
ne=Pout/(V0*I)
print 'Electronic efficiency: %0.3f'%(ne*100), '%'

#Overall efficiency
no=Pout/(Vc*I)
print 'Overall efficiency: %0.3f'%(no*100),'%'

Electronic efficiency: 26.667 %
Overall efficiency: 66.667 %


## Page Number: 334 Example 6.8¶

In [25]:

#Given
Vc=20e3  #V
V0=32e3  #V
Pout=75e3  #W
I=7  #A

#Electronic efficiency
ne=Pout/(V0*I)
print 'Electronic efficiency: %0.3f'%(ne*100),'%'

#Overall efficiency
no=Pout/(Vc*I)
print 'Overall efficiency: %0.3f'%(no*100), '%'

Electronic efficiency: 33.482 %
Overall efficiency: 53.571 %


## Page Number: 335 Example 6.9¶

In [26]:

#Given
I0=500e-3  #A
V0=10e3  #V
Z0=25  #ohm
l=.20  #m
f=5.93e9  #Hz

#Gain parameter
C=((I0*Z0)/(4*V0))**(1/3)
print 'Gain parameter: %0.3f'%C

N=(l*f)/(0.593e6*sqrt(V0))
#Gain
Ap=-9.54+(47.3*C*N)
print 'Gain of TWT: %0.3f'%Ap,'dB'

Gain parameter: 0.068
Gain of TWT: 54.656 dB


## Page Number: 335 Example 6.10¶

In [31]:

#Given
Pout=250  #W
n=0.15
V0=7.5e3  #V
f=6.15e9  #Hz
c=3e8  #m/s

#(i) Input Power
Pi=Pout/n
print 'Input Power: %0.3f'%Pi,'W'

#(ii) Beam current
I0=Pi/V0
print 'Beam current: %0.3f'%I0,'A'

#(iii) Beam velocity
vb=0.593e6*sqrt(V0)
print 'Beam velocity: %0.3f'%vb, 'm/s'

a=(2*vb)/(2*pi*f)

r=(3*a)/4
print 'Electron beam radius: %0.3f'%r, 'm'

#(vi) Pitch of helix
p=(2*pi*a*vb)/c
print 'Pitch of helix: %0.3f'%p,'m'

#(vii) Current density
J0=I0/(pi*r*r)
print 'Current density: %0.3f'%(J0/1000),'kA/msqr'

#(viii) Magnetic field for beam confinement
B=(4*8.3e-4*sqrt(I0/(r*r*sqrt(V0))))
print 'Magnetic field for beam confinement:' ,round(B*1000),'mT'

Input Power: 1666.667 W
Beam current: 0.222 A
Beam velocity: 51355306.444 m/s
Pitch of helix: 0.003 m
Current density: 17.799 kA/msqr
Magnetic field for beam confinement: 84.0 mT


## Page Number: 336 Example 6.11¶

In [33]:

#Given
I0=30e-3  #A
V0=3e3  #V
Z0=10  #ohm
l=0.1624  #m
f=10e9  #Hz
C=((I0*Z0)/(4*V0))**(1/3)
N=(l*f)/(0.593e6*sqrt(V0))

#Gain
Ap=-9.54+(47.3*C*N)
print 'Gain: %0.3f'%Ap,'dB'

ve=0.593e6*sqrt(V0)
be=(2*pi*f)/ve

#Four propogation constants
gam1=((-sqrt(3)*be*C)/2)+(1J*be*(2+C))/2
gam2=((sqrt(3)*be*C)/2)+(1J*be*(2+C))/2
gam3=1J*be*(1-C)
gam4=-1J*be*(1-((C*C*C)/4))

print 'Four propogation constants:\n {:.3f}\n{:.3f}\n{:.3f}\n{:.3f}\n'.format(gam1,gam2,gam3,gam4)

#Calculations for propogation constants are wrong for gam 3 and 4 hence answers dont match

Gain: 59.613 dB
Four propogation constants:
-48.986+1962.764j
48.986+1962.764j
0.000+1877.917j
0.000-1934.469j



## Page Number: 337 Example 6.12¶

In [34]:

#Given
I0=35e-3  #A
V0=4e3  #V
Z0=20  #ohm
f=10e9  #Hz

#(i) Gain parameter
C=((I0*Z0)/(4*V0))**(1/3)
print 'Gain parameter:' ,C

ve=0.593e6*sqrt(V0)
be=(2*pi*f)/ve

#Four propogation constants
gam1=((-sqrt(3)*be*C)/2)+(1J*be*(2+C))/2
gam2=((sqrt(3)*be*C)/2)+(1J*be*(2+C))/2
gam3=1J*be*(1-C)
gam4=-1J*be*(1-((C*C*C)/4))

print 'Four propogation constants:\n {:.3f}\n{:.3f}\n{:.3f}\n{:.3f}\n'.format(gam1,gam2,gam3,gam4)

#Calculations for propogation constants are wrong hence answers dont match

Gain parameter: 0.0352364936603
Four propogation constants:
-51.123+1704.826j
51.123+1704.826j
0.000+1616.278j
0.000-1675.292j